Wellbores are formed in subterranean formations for various purposes including, for example, extraction of oil and gas and extraction of geothermal heat from the subterranean formation. Wellbores may be formed in a subterranean formation using a drill bit such as, for example, an earth-boring rotary drill bit. Different types of earth-boring rotary drill bits are known in the art including, for example, fixed-cutter bits (which are often referred to in the art as “drag” bits), rolling-cutter bits (which are often referred to in the art as “rock” bits), diamond-impregnated bits, and hybrid bits (which may include, for example, both fixed cutters and rolling cutters). The drill bit is rotated and advanced into the subterranean formation. As the drill bit rotates, the cutters or abrasive structures thereof crush, shear, and/or abrade away the formation material to form the wellbore. A diameter of the wellbore drilled by the drill bit may be defined by the cutting structures disposed at the largest outer diameter, characterized in the art as the “gage diameter,” of the drill bit.
The drill bit is coupled, either directly or indirectly, to an end of what is referred to in the art as a “drill string,” which comprises a series of elongated tubular segments of drill pipe connected end-to-end that extends into the wellbore from the surface above the formation and commonly terminates at heavier-weight tubular drill collar segments. Often various tools and components, including the drill bit, may be coupled together at the distal end of the drill string at the bottom of the wellbore being drilled. This assembly of tools and components is referred to in the art as a “bottomhole assembly” (BHA).
The drill bit may be rotated within the wellbore by rotating the drill string from the surface, or the drill bit may be rotated by coupling the drill bit to a downhole motor, which is coupled to the drill string between the drill string and the drill bit proximate the bottom of the wellbore. The downhole motor may comprise, for example, a hydraulic Moineau-type motor having a shaft, to which the drill bit is mounted, that may be caused to rotate by pumping fluid (e.g., drilling mud or fluid) from the surface of the formation down through the center of the drill string, through the hydraulic motor, out from nozzles in the drill bit, and back up to the surface of the formation through the annular space between the outer surface of the drill string and the exposed surface of the formation within the wellbore.
During drilling of a wellbore, the rate of penetration (ROP) of the drilling operation is a parameter of significant interest. However, accurate measurement of ROP may be difficult to obtain using conventional means due to, among other issues, drill string flexing, elongation, and contraction as the drill bit proceeds through one or more subterranean formations exhibiting different rock characteristics. Such difficulty may be further exacerbated during directional and horizontal drilling, where large segments of the drill string may, at any one time, contact the wellbore wall and frictionally stick while the drill string rotates, followed by sudden release or “slip” when drill string torque overcomes frictional forces.